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Q2.

Expert-verified

Geometry

Found in: Page 485

Book edition Student Edition

Author(s) Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen

Pages 227 pages

ISBN 9780395977279

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Short Answer

Copy and complete the table below for the regular square pyramid.
$\begin{matrix} Height, h & 12 \\ Slant Height, l & 13 \\ Base edge \\ Lateral edge \end{matrix}$

$\begin{matrix} Height, h & 12 \\ Slant Height, l & 13 \\ Base edge & 10 \\ Lateral edge & \sqrt{194} \end{matrix}$

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Given information.

The height and slant height of a regular square pyramid are 12 and 13 unit respectively.

Step 2. Write the concept.

The base edge is given by:

$Base edge = 2 \sqrt{{(l)}^{2} - {(h)}^{2}}$

And the lateral edge is given by:

$lateral edge = \sqrt{{(l)}^{2} + {(\frac{base edge}{2})}^{2}}$

Step 3. Determine the values.

Substitute all the given values in the formula.

$\begin{matrix} Base edge = 2 \sqrt{{(13)}^{2} - {(12)}^{2}} [substitute] \\ = 2 \sqrt{169 - 144} [square] \\ = 2 \sqrt{25} [subtract] \\ = 10 [simplify] \end{matrix}$

And

$\begin{matrix} Lateral edge = \sqrt{{(13)}^{2} + {(5)}^{2}} [substitute] \\ = \sqrt{194} [simplify] \end{matrix}$

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